You can contact the Chilean embassy at Washington D.C (or the one in NY) to find out more information regarding this topic. http://www.chile-usa.org/
I think that the nation has unofficially requested TPS, but I do not think that the U.S will grant tps to Chileans. The reasons for this is because unlike Haiti, who is one of the poorest nations in the western hemisphere... Chile has had a very strong economy. For instance, because of the wise fiscal management of the two presidents before Pinera, Chile now has a surplus in revenue. It also has one of the world's lowest amount of national GDP (the debt burden is low). Hence, they not only have the funding to rebuild, but can finance their projects with a very low interest rate.
Ethically, it would be the right thing to do. It would be a politically smart move for President Obama in terms of showing Latino supports that he is with them. Realistically, it has already been more than 14 days and still no TPS... if it has not happened yet... chances are it probably will not. Haiti recieved TPS nine days after their earthquake...